
where \(d_{i,y}\)  and \(d_{i,z}\)  are the inter-element spacings for the horizontal and vertical elements in each \(i\) th R-RIS subarray. It is noted that, for quasi-free-space propagation conditions, fine-grained control over the reflected signals from each R-RIS subarray is essential for accurate reflective beamforming. This fact motivated researchers to rely on meta-atoms of sub-wavelength sizes [1]}, despite inevitable strong mutual coupling among those elements [2]}, [3]} (e.g., when the spacing of adjacent meta-atoms is \(\lambda /10\) ). In contrast, in rich scattering environments, the wave energy is statistically equally spread throughout the wireless medium, and \(\lambda /2\) -sized meta-atoms, and consequently inter-element spacing, suffice [4]}.
